A242104 Sum s of consecutive digits of Pi such that s is prime.

3, 5, 17, 11, 3, 5, 17, 7, 17, 47, 2, 7, 37, 17, 67, 29, 13, 11, 3, 7, 19, 89, 97, 19, 23, 43, 5, 5, 5, 23, 2, 5, 3, 5, 13, 11, 23, 7, 11, 13, 2, 7, 13, 13, 2, 2, 5, 5, 5, 19, 23, 53, 43, 47, 3, 3, 17, 19, 5, 23, 3, 7, 29, 3, 7, 5, 2, 7, 3, 19, 5, 5, 23, 23, 3, 13, 19, 13, 3, 2, 89, 7, 3, 7, 2, 17, 7, 131, 2, 5, 13, 17, 13, 13, 17, 2, 5, 19, 7, 5, 3, 5, 43, 2

Offset

1,1

Comments

A histogram of the first 1.4 million terms in this sequence reveals 7 as the most common term with a frequency of 15.25%. The smaller primes (2, 3, and 5) occur with frequencies between 12% and 14%, and larger primes rapidly decrease in frequency. 99% of the terms are composed of the first 20 primes (2, 3, 5, ..., 71). The largest of the first 1.4 million terms is a(220693) = 281, which is the sum of an otherwise prime-free sum of 64 consecutive digits of Pi (6 + 9 + 3 + 9 + 5 + 4 + 6 + 9 + 7 + 5 + 5 + 9 + 9 + 6 + 4 + 0 + 0 + 8 + 2 + 9 + 7 + 6 + 0 + 0 + 5 + 3 + 5 + 4 + 1 + 8 + 8 + 6 + 6 + 1 + 7 + 8 + 8 + 2 + 3 + 1+ 1 + 1 + 0 + 2 + 0 + 1 + 7 + 2 + 7 + 1 + 5 + 5 + 7 + 3 + 0 + 2 + 2 + 5 + 5 + 0 + 5 + 9 + 5 + 2).

Links

Table of n, a(n) for n=1..104.

Example

a(1) = 3 because it is the first digit of Pi, and it is prime.
a(2) = 1 + 4 = 5 because it is the sum of the next consecutive digits of Pi, and it is prime, and the prior sum (1) is not prime.
a(3) = 1 + 5 + 9 + 2 = 17 because it is the sum of the next consecutive digits of Pi, and it is prime, and prior sums (1, 1 + 5 = 6, 1 + 5 + 9 = 15) are not prime.

Crossrefs

Cf. A000040, A000796.

Sequence in context: A192911 A105408 A291963 * A158895 A085418 A339944

Adjacent sequences: A242101 A242102 A242103 * A242105 A242106 A242107

Keyword

nonn,base

Author

Gil Broussard, Aug 15 2014

Status

approved